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Voting Systems in Action

By       (Page 1 of 2 pages)   6 comments, In Series: Balanced Voting
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In the most recent previous article of this series we introduced another balanced voting system, BRV, that serves as an alternative system for those who consider' Balanced Approval Voting to be too complicated. In that a voter is asked to express an opinion about only one candidate, BRV is no more complicated than plurality voting. This is in sharp contrast to a voter being asked to express an opinion about every candidate as happens with BAV as in so many alternative voting systems.

But this concern for complexity may be overdrawn. Complexity of this sort is not the same thing as difficulty. Plurality voting is simple in the sense that the voter just picks one candidate to vote for, but picking that candidate may actually be quite challenging for many voters. There are many considerations to weigh in that choice and these issues may become clear as we explore a hypothetical election with a half-dozen candidates. Voters may find a more complex electoral system easier to deal with if it permits the voter to more accurately express how the voter feels about the candidates. Being pressured to think strategically about the election's outcome makes a voter's job much more difficult.

The example election we consider has six candidates that we will name Ri, La, Le, Li, Lo and Lu. Ri has the support of big business and importantly by big media and also supported by nearly 30% of likely voters. La, Le, Li, Lo and Lu pretty evenly split the remaining 70% of likely voters with each being supported by roughly 14%. Each of La, Le, Li, Lo and Lu represent particular issues that are of great interest to their voters so, while these voters nearly all consider Ri to be the last choice, their first-place choices also tend to be fairly rigid.

Plurality Voting:

PV is the most widely used system of voting and it is the system we all are familiar with. With PV, the voter is asked to choose the candidate he (or she) likes best and then vote for that candidate; this system might better be called First Choice Voting. But in practice and with good reason, voters do not always do what they are told. They often do not vote for their actual first choice but rather for their first choice just among the candidates considered to have a good chance of winning the election.

With PV, the candidate Ri clearly has an unsurmountable advantage with a wide lead over any of the other candidates. Unfortunately though, this means that the candidate most strongly opposed by about 70% of the voters will win election will win. The media will of course avoid making any of the other candidates stand out from the pack and this will leave voters with little guidance regarding which of La, Le, Li, Lo and Lu might be the most likely of them to win election. Ri would seem to be a shoe-in with this traditional voting system.

Balanced Plurality Voting:

With BPV, the voter is asked to choose one candidate but in this case it should be the candidate the voter is most concerned about, not necessarily the candidate likes the most. The voter can cast a vote for that candidate or against that one candidate and we will see that the outcome of the election will depend significantly on that decision. Clearly, the supporters of Ri will vote for Ri, if only because they would not know which of the other candidates to vote against. But the 70% of voters who support the other candidates all share an opposition to Ri so some might choose to vote against Ri instead of for their favorite candidate. Many would likely recognize that if they vote support, say for Lo then their vote would help Ri to win; however voting against Ri would also help Li win against Lo so it is a difficult choice for the voter to make.

If 10% of the voters decide to vote against Ri then the net vote for Ri would drop to 20% (= 30% - 10%) but Ri would still win if, as would likely happen, that 10% were evenly divided among the other candidates. Each would each be supported by only 12% ( = 14% - 2%) of the voters. The outcome become a toss-up, however, when around 20% of the voters decided to vote against Ri. Ri's net vote would drop to 10% (= 30% - 20%) in this case while the average net vote for the other candidates would rise to 10%. But if more than 20% of the voters chose to vote against Ri then there would be no way for Ri to win.

Ri's supporters will obviously want everyone to vote for the candidate they most like. Whether they might try to influence voters in that direction with up-beat slogans like Vote for the Candidate you Really Like or Don't be Negative or whether they might instead just focus on selective voter suppression is hard to predict. They might well use both tactics; the only certainty is that some supporters of Ri will lose sleep trying to figure out what is the best way to defeat the will of that troublesome 70% of voters.

Balanced Approval Voting:

With BAV, a voter is asked to evaluate every candidate by marking the ballot as Approve or Disapprove for each one . When the ballots are counted, a tally is made for each candidate of the number of ballots marked Approve and the number marked Disapprove and the net vote for a candidate is the difference (the number of Approve less the number of Disapprove). The candidate with the largest net vote wins the election.

In our hypothetical election, about 30% of the voters will Approve of Ri while about 70% will disapprove so Ri will have a net vote of -40%. Each of La, Le, Li, Lo and Lu will each have roughly the same vote tallies of about +14% of the ballots, essentially a five-way tie while Ri runs a distant sixth place.

The negative net vote that Ri receives is a clear reflection of the fact that more voters disapprove of Ri than approve of her (or him). But it is worth recalling that with plurality voting, Ri would win and even with BPV, Ri there is a good possibility that Ri might win. With BAV there is much more certainty that a dramatically unpopular candidate could not possibly win election.

As for how the media might try to tip the scale for Ri with BAV it is hard to say and that alone seems to be a good thing. Unfortunately, changing the voting method cannot avoid the hazards of voter suppression and other forms of outright election fraud. Participation of more viable candidates does seem to make election fraud more complicated and perhaps even a bit more difficult, however.

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Attended college thanks to the generous state support of education in 1960's America. Earned a Ph.D. in mathematics at the University of Illinois followed by post doctoral research positions at the Institute for Advanced Study in Princeton. (more...)

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